Drude weight and dc-conductivity of correlated electrons

TL;DR

This paper provides a theoretical analysis of the Drude weight and dc-conductivity in strongly correlated electron systems, showing finite conductivity at all temperatures and Fermi liquid behavior in the Hubbard model in infinite dimensions.

Contribution

It derives analytic results for the Hubbard model and spinless fermions in infinite dimensions, including $1/d$ corrections, and discusses the implications for finite-dimensional systems.

Findings

dc-conductivity is finite for all T > 0, showing Fermi liquid behavior

Analytic expressions for the Hubbard model in infinite dimensions

Finite dc-conductivity is a generic feature in not too low dimensions

Abstract

The Drude weight $D$ and the dc-conductivity $\sigma_{dc} (T)$ of strongly correlated electrons are investigated theoretically. Analytic results are derived for the homogeneous phase of the Hubbard model in $d = \infty$ dimensions, and for spinless fermions in this limit with $1/d$-corrections systematically included to lowest order. It is found that $\sigma_{dc}(T)$ is finite for all $T > 0$, displaying Fermi liquid behavior, $\sigma_{dc} \propto 1/T^2$, at low temperatures. The validity of this result for finite dimensions is examined by investigating the importance of Umklapp scattering processes and vertex corrections. A finite dc-conductivity for $T > 0$ is argued to be a generic feature of correlated lattice electrons in not too low dimensions.